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Weekly_002.SOLN

# Weekly_002.SOLN - Phys 274 c Eric B Szarmes Weekly Homework...

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Phys 274 – c Eric B. Szarmes 31 January 2011 Weekly Homework 002 SOLUTIONS Problem 1 – Q2S.12 If Legolas can discern hair color between two people far away, then he can resolve distances down to about the width of a head (so that he can discern a yellow blob from, say, a brown blob, and count riders who may be sitting beside one another.) Take the width of a head to be 1 ft = 0 . 30 m, and assume that this is also the minimum separation d between two heads. Also, take λ = 590 nm for yellow light. The resolution problem is depicted in the figure below. a ! ! D d head 1 head 2 In the problem, we are given D 15 mi 24 km. How large would Legolas’ eyes have to be in order for him to resolve an object of width 0.30 m at this distance? The resolution criterion requires that the minimum angular separation α min equal the angle θ 1 d of the first null in the diffraction pattern: sin α min = sin θ 1 d = 1 . 22 λ a or α min = 1 . 22 λ a (1) for small angles, where a is the diameter of Legolas’ pupils and α min = d/D . Solving for the diameter

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